Certifying Algorithms for Recognizing Interval Graphs and Permutation Graphs

Authors:
Dieter Kratsch;Ross M. McConnell;Kurt Mehlhorn;Jeremy P. Spinrad
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Computing
Year:
2006

Citing 0
Cited 14

Minimal comparability completions of arbitrary graphs

Discrete Applied Mathematics
A polynomial-time algorithm for the paired-domination problem on permutation graphs

Discrete Applied Mathematics
Linear-time certifying recognition algorithms and forbidden induced subgraphs

Nordic Journal of Computing
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs

Discrete Applied Mathematics
A Certifying Algorithm for 3-Colorability of P5-Free Graphs

ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Approximation and fixed-parameter algorithms for consecutive ones submatrix problems

Journal of Computer and System Sciences
The LBFS Structure and Recognition of Interval Graphs

SIAM Journal on Discrete Mathematics
Certifying algorithms for recognizing proper circular-arc graphs and unit circular-arc graphs

WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Making arbitrary graphs transitively orientable: minimal comparability completions

ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
Certifying algorithms for the path cover and related problems on interval graphs

ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part II
Survey: Certifying algorithms

Computer Science Review
An O(nm)-time certifying algorithm for recognizing HHD-free graphs

Theoretical Computer Science
Every DFS Tree of a 3-Connected Graph Contains a Contractible Edge

Journal of Graph Theory
Normal Helly circular-arc graphs and its subclasses

Discrete Applied Mathematics

Quantified Score

Hi-index	0.00

Visualization

Abstract

A certifying algorithm for a problem is an algorithm that provides a certificate with each answer that it produces. The certificate is a piece of evidence that proves that the answer has not been compromised by a bug in the implementation. We give linear-time certifying algorithms for recognition of interval graphs and permutation graphs, and for a few other related problems. Previous algorithms fail to provide supporting evidence when they claim that the input graph is not a member of the class. We show that our certificates of nonmembership can be authenticated in O(|V|) time.